[填空题]
A population of 50 hamsters was introducefklzu;eacp6;7 */ccyb i;pr-vce 2 1rd to a new town. One monthxb5ln yv 0d;7otg3v t4 later, the nuvdt7 tbyxv03n og;5 l4mber of hamsters was 62 . The number of hamsters, P , can be modelled by the function
P(t)=50 $\times b^{t}, \quad t \geq 0$
where t is the time, in months, since the hamsters were introduced to the town.
1. Find the value of b .
2. Calculate the number of hamsters in the town after 6 months.
A wildlife specialist estimates that the town has enough water and food to support a maximum population of 2000 hamsters. ≈
3. Calculate the number of months it takes for the hamster population to reach this maximum. ≈
